What is a model and how is it designed?
A model is exactly what the name suggests.  A simplified representation of a solution to a real life problem.

For example, if you think of a simple formula for a falling object you may not take into account real life variables such as the imperfections on the surface of the object, atmospheric conditions, the exact composition of the air the object is falling through and how it may affect friction.  you just use a simple model to "model" the fall and get a reasonably accurate result.  its a model, it doesnt have all the details.  just like a model car wouldnt have all the details of a real car.

Here's a good read to get you started:
https://en.wikipedia.org/wiki/Mathematical_model